2010/09/16 by Damir D. Dzhafarov, Dzhafarov, Damir D., Carl Mummert +1
Computer Science · Mathematics · #03B30 (Primary) 03F35 #03D45 (Secondary) #Advanced Topology and Set Theory #Complexity and Algorithms in Graphs #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1009.3242
openalex publication_date 2010/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the reverse mathematics of countable analogues of several maximality principles that are equivalent to the axiom of choice in set theory. Among these are the principle asserting that every family of sets has a ⊆-maximal subfamily with the finite intersection property and the principle asserting that if P is a property of finite character then every set has a ⊆-maximal subset of which P holds. We show that these principles and their variations have a wide range of strengths in the context of second-order arithmetic, from being equivalent to Z2 to being weaker than ACA0 and incomparable with WKL0. In particular, we identify a choice principle that, modulo Σ02 induction, lies strictly below the atomic model theorem principle AMT and implies the omitting partial types principle OPT.